Geometric and functional inequalities play a crucial role in several
problems arising in the calculus of variations, partial differential
equations, geometry, etc.
More recently, there has been a growing interest in studying the stability
for such inequalities.
The basic question one wants to address is the following: suppose we are
given a functional inequality for which minimizers are known. Can we prove
that if a function “almost attains the equality” then it is close (in some
suitable sense) to one of the minimizers?
The aim of this talk is to describe some ways to attack this kind of
problems, and to show some applications.
The talk is intended to be accessible to graduate students.